In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different assumptions. Especially, the case of bang-bang controls is investigated. Numerical examples are provided to illustrate the results.


  1. time-optimal control
  2. error estimates
  3. Galerkin method
  4. bang-bang controls

MSC codes

  1. 49K20
  2. 49M25
  3. 65M15
  4. 65M60

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Information & Authors


Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1730 - 1756
ISSN (online): 1095-7138


Submitted: 13 September 2018
Accepted: 18 March 2019
Published online: 21 May 2019


  1. time-optimal control
  2. error estimates
  3. Galerkin method
  4. bang-bang controls

MSC codes

  1. 49K20
  2. 49M25
  3. 65M15
  4. 65M60



Funding Information

Austrian Science Fund https://doi.org/10.13039/501100002428
Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659

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